The punctual Hilbert scheme

Specialeforsvar ved Josh Cohen

Titel: The punctual Hilbert scheme

Abstract: The punctual Hilbert scheme parametrizes the 0-dimensional subschemes of length $n$ of a given scheme. Such a subscheme might be a collection of distinct points, more complicated subschemes arise when some points collide. We will consider how these geometric properties are reflected in the Hilbert scheme, and vice versa. In most situations the Hilbert scheme has a very pathological structure, however in low dimensions it is possible to compute. In particular we look first at smooth curves and surfaces, which in fact give rise to smooth Hilbert schemes. Then we consider three simple curve singularities, the node, cusp and triple crossing.

Vejleder: Lars Halvard Halle
Censor: Pieter Beelen